
where \(\sigma _{\mu \nu }=\frac{i}{2}(\gamma _{\mu }\gamma _{\nu }-\gamma _{\nu }\gamma _{\mu })\) , \({\cal {F}}_{\mu \nu }=\partial _{\mu }{\cal {A}}_{\nu }-\partial _{\nu }{\cal {A}}_{\mu }\) ,
and \(\epsilon _{\mu \nu \alpha \beta }\)  is the Levi-Cività tensor with \(\epsilon _{0123}=1\) . \(N\) , \(V\) , \({\cal {A}}\) , and \(\eta _1\)  are the nucleon, vector mesons, photon, and \(\eta _1(1855)\)  meson fields, respectively. \(m_N\)  represents the
masses of the nucleon. The coupling constants for vertexes \(\rho {}NN\)  and \(\omega {}NN\)  are taken from the analyses of \(\pi \)  photoproduction, \(\omega \)  photoproduction,
nucleon-nucleon scattering, and \(\pi -N\)  scattering [1]}, [2]}, [3]}
\(&g_{\omega {}NN}=10.35,~~~~~ \kappa _{\omega }=0, \nonumber \\&g_{\rho {}NN}=6.12, ~~~~~~~ \kappa _{\rho }=3.1.\nonumber \) 
